Hyperbolic [[Function|Functions]] are the analogue of [[Trigonometry|Trigonometric Functions]] for [[Hyperbolic Space]].
$\huge
\begin{align}
\sinh (x) &= \frac{e^x-e}{2}\\
\cosh (x) &= \frac{e^x+e}{2}\\
\tanh (x) &= \frac{e^x-e}{e^x+e}\\
\end{align}
$